I would recommend the 2506. The 24120 wouldn't be a good fit for this implementation. Such a high-gain omnidirectional antenna may cause the signal to overshoot your remote sites. And yes, the internal antennas for the remote sites will be fine. The internal antenna is pretty strong and can go at least a kilometer. 200m is cake for it.
Best practice is to use the provided antenna cable length, and to not lengthen it. You can certainly do what you're suggesting, but depending on your coax length you'll lose quite a bit of signal doing so.
The double-coax (from the bridge to the power injector) and Ethernet cables can each be up to 100m in length, without any kind of loss. As such, best practice would be:
Antenna mounted to mast
Bridge mounted to mast
<100m of double-coax (runs inside)
Power injector (mounted inside)
<100m of Ethernet (runs to data closet)
If you want to consider installing the bridge in your pop and running the antenna cable up the mast, just find out what kind of loss you'll see. Any coax manufacturer, Cisco or otherwise, will say what the dB/foot or dB/meter is, so you can know exactly how much you'll lose to the cable length. I would recommend against the design though, since you might need a larger antenna which will result in broadcasting a pretty noisy signal.